Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4595550 | Journal of Number Theory | 2007 | 9 Pages |
Abstract
Let F(z)∈R[z] be a polynomial with positive leading coefficient, and let α>1 be an algebraic number. For r=degF>0, assuming that at least one coefficient of F lies outside the field Q(α) if α is a Pisot number, we prove that the difference between the largest and the smallest limit points of the sequence of fractional parts {F(n)αn}n=1,2,3,… is at least 1/ℓ(Pr+1), where ℓ stands for the so-called reduced length of a polynomial.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory